"We are dealing with the serious risk that the eurozone will fall apart," said Nicholas Spiro, managing director of London-based consultancy Spiro Sovereign Strategy. "And Greece is the trigger."

While the Greek economy is small, the fear is that continued political turmoil there could result in Greece exiting the euro currency union. That could drag down other fragile euro area nations and shock the financial system at a time when the global economy is weak.

Greece has been without a fully functioning government since May 6, when voters last went to the polls. After the three main parties all failed to form a coalition government, a second election was called for June 17.

The concern is that Sunday's election will play out like the last one, leaving Greece with a weak caretaker government at a time when the nation needs clear leadership.

Greece must identify additional budget cuts by the end of June to be considered 'compliant' with the terms of its bailout program. If it fails to do so, analysts say the European Central Bank could cut off funding to Greek banks, which have already been drained of cash as deposits flee the country.

In addition, Greece is facing a €3.9 billion bond redemption in August, which it could struggle to pay if there is still no government in place by then.

The Greek economy is in deep decline and analysts say Athens is in danger of running out of the money it needs to pay for basic necessities, such as fuel and medical supplies.

"They clearly don't have the cash to cover basic services," said Spiro. "The country is bankrupt."

Syriza, the radical left-wing party, came in second in the last election as voters skewed toward politicians who oppose more austerity. Syriza's leader, Alexis Tsipras, has threatened to renege on the terms of Greece's bailout, but he has also expressed a desire to remain in the euro currency union.

The moderate New Democracy party and the Socialist Pasok party were punished by voters for supporting the bailout program, and agreeing to the austerity measures that came with it.

There was a ban on polls in the run up to the vote, but surveys taken last month showed a tight race between Syriza and New Democracy.

The election is being framed as a potential catalyst for Greece to exit the euro zone. But none of the main political parties is eager to see that happen, since returning to the drachma would have severe and unknowable consequences for Greece.

"No political party from the left or the right will risk taking the country out of the eurozone," said Dimitri Papadimitriou, a professor of economics at Bard College.

Jose Barroso, president of the European Commission, said Wednesday that he wants Greece to stay in the euro area "assuming it will respect its commitments." But he criticized European leaders for underestimating the depth of the crisis in the eurozone.

"We have a systemic problem and we need to articulate the vision of where we need to go," Barroso told the European Parliament. "I am not sure whether the urgency of this is fully understood."

While the outcome is impossible to predict, analysts say any government that comes to power will seek to renegotiate the terms of Greece's bailout. And there are signs that Germany and other fiscal hawks will be willing to make concessions, given the fragility of Spain and Italy.

"The finishing touches are being placed on a package of concessions to Greece's second bailout that will be discussed with any incoming government, assuming one is formed and irrespective of what it looks like," said Mujtaba Rahman, an analyst at political research firm Eurasia Group.

In a research report, Rahman wrote that in the unlikely event that no government is formed, EU policymakers have a number of options to deal with Greece's upcoming €3.9 billion bond redemption in August. For example, he pointed to the €35 billion that was provided to the ECB as part of Greece's debt restructuring.

"In the context of an inconclusive result, some workaround for the bond redemption would be agreed," said Rahman.

Meanwhile, the uncertain situation in Greece could have serious repercussions for other troubled euro area economies.

Investors have also set their sights on Italy, driving up the nations borrowing costs amid fears the crisis is spreading to the core of the eurozone.

"It's quite clear this is spreading," said Jennifer McKeown, senior European economist at Capital Economics. "Spain's bailout is at least encouraging, but I hope they will put something together for Italy as well."